Final year Project I

UNIVERSITY OF DAR ES SALAAM

COLLEGE OF ENGINEERING AND TECHNOLOGY

DEPARTMENT OF WATER RESOURCES ENGINEERING

ASSESSMENT OF THE ADEQUACY OF EXISTING CROSS

DRAINAGE STRUCTURE AT MABATINI, ALONG MWANZA-
MUSOMA ROAD

NAME: SELEKA, MIKE

REG NO: 2016-04-03520
SUPERVISOR: DR. JOSEPH O. MTAMBA
Final year Project I
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CERTIFICATION
The undersigned certifies that he read and hereby recommends for examination by the
University of Dar es Salaam a project entitled assessment of the adequacy of existing cross
drainage structure at Mabatini, along Mwanza-Musoma road, in partial fulfillment of the
requirements for the degree of Bachelor of Science in Civil Engineering at the University of Dar
es Salaam.

………………………………………………………
Dr. J. O. Mtamba

Date: ………………………….

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DECLARATION AND COPYRIGHT

I, Seleka Mike, declare that this project is my original work and that it has not
been presented and will not be presented in any other University for a similar or any other
degree award.

Signature: …………………………

Date: ………………………………

This project is a copyright material protected under the Berne Convention, the Copyright
Act 1999 and other international and national enactments, in that behalf, on the intellectual
property. It may not be reproduced by any means, in full or in part, except for short extracts
in fair dealing, for research or private study, critical scholarly review or discourse with
acknowledgement, without written permission of the author or the Directorate of
Undergraduate Studies, on behalf of both the author and the University of Dar es Salaam

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DEDICATION

I dedicate this report to Mr. and Mrs. Seleka for devoting their support and encouragement.
I do also dedicate this project to my sisters Irene, Elizabeth and Catherine and to brother Daniel
for their prayers and cooperation to my field of study. May our Almighty God
bless you all.

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TABLE OF CONTENTS
CERTIFICATION ...................................................................................................................... i
DECLARATION AND COPYRIGHT ....................................................................................... ii
DEDICATION .......................................................................................................................... iii
TABLE OF CONTENTS ............................................................................................................v
LIST OF FIGURES ................................................................................................................. vii
LIST OF TABLES .................................................................................................................. viii
LIST OF ABBREVIATIONS.................................................................................................... ix
CHAPTER 1: INTRODUCTION ................................................................................................1
1.1 General background ...........................................................................................................1
1.2 Problem statement .............................................................................................................2
1.3 Objectives ..........................................................................................................................3
1.3.1 Main objective.............................................................................................................3
1.3.2 Specific objectives.......................................................................................................3
1.4 Scope of the study ..............................................................................................................3
1.5 Significance of the study ....................................................................................................3
CHAPTER 2: LITERATURE REVIEW .....................................................................................4
2.1 Introduction .......................................................................................................................4
2.2 Hydrology .........................................................................................................................4
2.3 Precipitation.......................................................................................................................4
2.3.1 Analysis of rainfall data ...............................................................................................5
2.4 Estimation of design discharge ...........................................................................................7
2.4.1 Methods of estimate the Design Discharge ..................................................................7
2.4 Method of sizing cross drainage structures ....................................................................... 18
2.4.1 Manning’s equation ................................................................................................... 18
2.4.2 Nomograph ............................................................................................................... 19
2.5 Performance analysis of drainage structure ...................................................................... 21
2.5.1 Hydraulic Performance of Culvert ............................................................................. 21
2.5.2 Location of Culverts .................................................................................................. 21
2.5.3 Deposition in the culvert............................................................................................ 22
2.5.4 Inlet and outlet controls ............................................................................................. 22
2.5.5 Energy Dissipation .................................................................................................... 23
CHAPTER 3: DATA AND METHODOLOGY ........................................................................ 24

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3.1 Description of Project Area .............................................................................................. 24

3.1.1 Location .................................................................................................................... 24
3.1.2 Topography ............................................................................................................... 25
3.1.3 Demographic Characteristics in Mwanza ................................................................... 25
3.1.4 Climate...................................................................................................................... 25
3.2 Desk study ....................................................................................................................... 25
3.3 Field investigation ........................................................................................................... 26
3.3.1 Field investigation data.............................................................................................. 26
3.4. Estimation of design discharge at the location of assessment. .......................................... 27
3.4.1 Data Required and Collection .................................................................................... 27
3.4.2Data analysis .............................................................................................................. 30
3.5 Propose of appropriate size of cross drainage structure. .................................................... 31
References ................................................................................................................................ 33
Appendex 1: Map of Cathcment Area ....................................................................................... 34
Appendex 2: Form of Assessing Condition of Culvert ............................................................... 35
Appendex 3: Soil Zone.............................................................................................................. 36
Appendix 4: Rainfall Zone ........................................................................................................ 37
Appendix 5: Rating System ....................................................................................................... 38
Working Plan and Budget ......................................................................................................... 39

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LIST OF FIGURES

Figure 1:Existing cross drainage structure, upstream condition, 2020 ..........................................2

Figure 2: Graph Showing The Different Behavior Of Extreme Value Type: ................................6
Figure 3: Idf Curve......................................................................................................................9
Figure 4: Nomograph ................................................................................................................ 20
Figure 5: Map Of A Project Area .............................................................................................. 24

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LIST OF TABLES
Table 1: Kerby’s Roughness Parameter ..................................................................................... 10
Table 2: Runoff Coefficient....................................................................................................... 11
Table 3: Catchment Lag Times.................................................................................................. 14
Table 4: Standard Contributing Area Coefficients .................................................................... 14
Table 5: Catchment Wetness Factor .......................................................................................... 14
Table 6: Land Use Factors......................................................................................................... 14
Table 7: Rainfall Time For East African .................................................................................... 15
Table 8: Manning's Coefficients ................................................................................................ 19
Table 9: Manning's Coefficients ................................................................................................ 32

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LIST OF ABBREVIATIONS

GIS Geographic Information System

DEM Digital elevation Model
SRTM Shuttle Radar Topography Mission
EVI Extreme value Type I
EVII Extreme value Type II
EVIII Extreme value Type III
TRRL Transport and Road Research Laboratory
IDF Intensity Duration Frequency Curve
UH Unit Hydrograph
ER Effective Rainfall
DRH Direct Runoff Hydrograph
FHWA Federal Highway Administration
m Meter
m2 Square meter
km Kilometer
km2 Square kilometer

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CHAPTER 1: INTRODUCTION
1.1 General background

Mwanza town was founded in 1892 as a Regional Administration and Commercial Centre to
control mainly export production of the cotton growing areas in the Lake Victoria Zone. In 1980
Mwanza obtained the status of municipality in line with the local government structure established
in 1972. In 2000, Mwanza was further promoted to a City status (Mwanza Region Socio-
Economic Profile, 2017). Mwanza-Musoma road is a trunk road, such that it connects the Mwanza
and Mara region. Mabatini is a ward which is in Nyamagana district at Mwanza region.

The rainfall at Mwanza is distributed mainly into two annual wet seasons. There is a long rainy
season from March to May and a short rainy season from October to December. However, the
shorter rainy season sees substantially heavier rainfall per month, with November typically seeing
the heaviest amount of precipitation at an average of around 180 mm of rain (Mwanza Region
Socio-Economic Profile, 2017). During rainfall seasons most of drainage structure at Mwanza are
inadequate due to poor maintenance programs also change in climatic condition (MWAUWASA,
2013).

Drainage is the natural or artificial removal of surface and subsurface water from a given area.
Drainage limits and controls damage from flooding to ensure the surface water system performs
satisfactorily. Overtopping of a drainage structure can be caused by various factors such as change
in environmental condition, change of land use for example urbanization, removing of vegetation.
Due to the factors which cause flooding, it results to increase in runoff to the streams. Increase of
discharge in a stream beyond its capacity results to fail of the performance drainage structures.

The figure 1 below shows the condition of upstream (inlet). From the figure 1, it can be observed
that the drainage has a lot of trashes which they reduce the capacity of a drainage, also there is
high sedimentation which leads to reduce the capacity of the opening and performance of the
drainage structure. Also, there is a crossing pipe below the deck of the culvert which reduces the
capacity of the existing box culvert.

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Figure 1:Existing cross drainage structure, upstream condition, 2020

1.2 Problem statement

Mirongo river is a seasonal river. The river crosses Mwanza-Musoma road at different locations.
Due to poor performance of existing cross drainage structure which is box culvert located at
Mabatini area along Mwanza- Musoma road cause the water to overtop the drainage structure. The
water that overtop the existing drainage structure passes through the road. due to overtopping of
the box culvert the road is temporally closed. The close of road results to the increase of traffic
congestion, cause people to use alternative road which increases both travel time and transportation
cost. The water which overtop the culvert passes through the road at high speed it increases
deterioration of road pavement by washing away the wearing course of the pavement. Assessment
of the adequacy of existing cross drainage structure should be carried out so as to propose an
engineering solution toward the existing problem.

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1.3 Objectives

1.3.1 Main objective

The objective of this project is to assess the adequacy of existing cross drainage structure at
Mabatini along Mwanza-Musoma road.

1.3.2 Specific objectives

The specific objective of this study is

a) To estimate the design discharge that pass at the location of assessment.
b) To propose appropriate size of drainage structure that will pass the design discharge at
the location of assessment.

1.4 Scope of the study

The study involves determination of design discharge at the location of assessment and propose
appropriate size of opening that will pass the design discharge adequately.

1.5 Significance of the study

The study will help to propose an engineering solution toward existing problem.

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CHAPTER 2: LITERATURE REVIEW

2.1 Introduction

This chapter reviews necessary knowledge and theories to be used in analysis of hydrology,
hydraulic design of structures and assess the performance of the structure. This will comprise the
revision of well-established scholarly articles, books and other sources relevant to a particular
issue, area of research, or theory, providing a description, summary, and critical evaluation of each
work. The purpose is to offer an overview of significant literature published on a topic. The aim
of literature review is to explore the background of the problem and the extent of existence. So,
basically this chapter is divided into three categories, these are hydrology, hydraulic and condition
assessment of drainage structure especially culvert.

2.2 Hydrology

According to (Chow, 1988) Hydrology is an applied science concerned with the water of the earth
in all its states; i.e. their accuracies distribution, and circulation through the unending hydrological
cycle of precipitation, consequent runoff stream flow, infiltration and storage, and eventually
evaporation and precipitation. Hydrology plays a great role in design, planning and construction
of hydraulic structures since enable engineer to design efficient and economical structures. or
deterministic and partly random. Such a process is called stochastic process. In some cases, the
random variability of the process is large compared to its deterministic variability that the
hydrologist is justified in treating the process as purely random. When there is no correlation
between adjacent observation the output of hydrologic system is treated as stochastic, space
independent and time independent in the classification scheme. This type of treatment is
appropriate for observations of extreme hydrologic events such as floods or droughts and for
hydrologic data averaged over long time intervals such as annual precipitation.

2.3 Precipitation

Precipitation is major factor that contribute to the surface runoff. Evaporation of water from
exposed water surface like streams, rivers, oceans, ponds also from land and plants which is in
form of water vapor collected by the atmosphere and behaves like a gas. Evaporation of water
continue increase the amount of atmospheric vapour. Atmosphere can hold a certain fixed amount
of water vapour. When than amount is reach any further addition of vapour will get condensed on
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surfaces as precipitation. Precipitation is the water which returns to the surface of the earth in
various form such as rain, snow, hail etc. the major part of precipitation occurs in form of rain and
the minor part in form of snow, other forms of precipitation are generally ignored in hydrological
work since they are not important (Chow, 1988).

2.3.1 Analysis of rainfall data

2.3.1.1 Introduction

Design Frequency or return period is indicative of the frequency with which a certain magnitude
of rainfall/runoff occurs within that period (Raghunath, 2006). It is the number of times a flood of
a given magnitude can be expected to occur on average over a long period of time. Design
frequency can be expressed with probability. The probability of being equal or exceeded in any
year can be defined by the following expression:

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P (X ≥ XT) = (Chow, 1988)
T

Where: P = Frequency of Exceedance

T = Occurrence of design flood exceeded or equaled once (return period), in years

Since it is not economically feasible to design a structure for the maximum runoff a watershed is
capable of producing, a design frequency must be established according to the cost, potential flood
hazard to property, expected level of service, social and political considerations, and budgetary
constraints, and considering the magnitude and risk associated with damages from inundation.
Analysis of rainfall data involve determination of design rainfall storm. Design rainfall storm is
the rainfall depth associated with given average recurrence of interval and duration. The estimation
of rainfall design storm can also be determined by using frequency analysis using extreme rainfall
data. The design storm for different frequencies of occurrences such as 5, 10, 25, 50 and 100 year
of return periods. If the data of long period is obtained from self-recording raingauge, the intensity
of rainfall at specified duration can be determined through frequency of occurrence which
generated IDF curve.

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2.3.1.2 Method used in determining design rainfall storm

The study of extreme hydrologic events involves the selection of sequence of largest (maximum)
or smallest (minimum) observations from a set of data (Chow, 1988). There are main three forms
of extreme values namely Type I, Type II and Type III. These types were developed by different
people. Type I is called Gumbel distribution extreme value (EVI), Type II is for Fréchet
distribution (EVII) and type III is called Log-Pearson distribution (EVIII). Frequency analysis of
the data should be performed to check under what type of extreme value distribution is fitting as
shown in figure 2.

Figure 2: graph showing the different behavior of extreme value type (Chow, 1988).
Rainfall data the common method which is used is extreme type I because of no bound to variety
of rainfall depth. The method which is used to estimate the design rainfall storm is called Gumbel’s
distribution (Subramanya, 2008; Chow, 1988).

General equation Gumbel distribution in hydrologic frequency analysis. The equation is given as
the cumulative density function F(X):

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x−u
−( )
−e α
F(x) = e

Where u = mode of the distribution

α = Scale parameter

A reduced variety y at certain return period (T) is called a frequency factor which can be defined
as (Subramanya, 2008).
𝑇
𝑦𝑇 = − 𝑙𝑛 [𝑙𝑛 ( )]
𝑇−1
The prediction equation of design rainfall storm is given as:

XT = u + .yT
Where XT = rainfall storm magnitude of a certain return period.
yT = Frequency factor.

The estimation of parameter from method of moment gives

−
Mean: 𝑥 = 𝑢 + 0.5772𝛼
standard deviation: 𝑠 = 1.28𝛼

The following are procedures for determining design rainfall storm corresponding to return
period using annual maximum rainfall data.

a) Arrange your data in chronological order and note the sample size
b) Calculate the mean and standard deviation of the sample
c) Use the table to find the reduced mean and standard deviation
d) Calculate the reduced variate
e) Also calculate the value of frequency factor
f) Then calculate the value of the variate X of a random hydrologic series with a return period,
XT. (Subramanya, 2008)

2.4 Estimation of design discharge

2.4.1 Methods of estimate the Design Discharge

The design discharge is the quantity of water which passes at the outlet point of a catchment which
is used in designing the appropriate size of hydraulic structure. In design of discharge, the choice

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of method to be used is affected by the hydrological data available in a particular area. Also, the
design discharge can be used to check the capacity of existing hydraulic structure if it can pass
safely without problems. There are several methods used in estimate the design discharge for
drainage structures. These methods are Rational Method, Time-Area method, Unit-Hydrography,
Empirical methods and Transport and Road Research Laboratory (TRRL).

2.4.1.1 Rational method

This is the method used to estimate peak discharge for small watershed (catchment area) and for
ungauged catchments. The method is used to find the discharge when the catchment area is less
than 1.2 km2 (Raghunath, 2006). Rational method formula for finding design flood is given by:

CIA
Q=
3.6

Where:
Q is the peak runoff rate (m3/s)
C is runoff coefficient, no dimensional
I is rainfall intensity (mm/hr.)
A is catchment area (km2)
The following are the basic requirements for using rational method
a) Intensity-Duration-Frequency curves (IDF curves)

IDF curves provides a summary of a site's rainfall characteristics by relating storm

duration and exceedance probability (frequency) to rainfall intensity which is assumed
to be constant over the duration (Raghunath, 2006).To interpret an IDF curve, find the
rainfall duration along the x-axis which is assumed to be concentration time this is
because all parts of watershed are contributing to the outlet point of discharge then go
vertically up the graph until reaching the proper return period, then go horizontally to
the left and read the intensity off the y-axis. The example of IDF curve is shown in
figure 3.

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Figure 3: IDF curve (Source Bangkok Metropolis Station)

b) Time of concentration

The time of concentration is the duration of rainfall required to produce the maximum
rate of runoff from the most remote region of watershed to reach the point of
concentration at which the flow is to be calculated (Stormwater Drainage Manual,
2018). The time at which entire catchment will contribute to the runoff at the outlet will
help us to decide the intensity of a rainfall. Basically, there are two formulas which are
used in calculating the concentration time

i. Morgali and Linsley Method

For small urban areas with drainage areas less than ten or twenty acres, and for
which the drainage is basically planar, the method developed by Morgali and
Linsley (1965) is useful. It is expressed as.

Tc = 0.94(nL)0.6
i0.4 S0.3
Where: Tc = time of concentration (min),
i = design rainfall intensity (in/hr),
n = Manning surface roughness (dimensionless),

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L = length of flow (ft), and

S = slope of flow (dimensionless).

ii. Kirpich Method

For small drainage basins that are dominated by channel flow, the Kirpich (1940)
equation can be used. Some authors use an adjustment factor for the Kirpich
approach to correct for paved channels. The Kirpich method is limited to watershed
with a drainage area of about 200 acres. The Kirpich equation is

Tc = 0.0078(L3/h)0.385

Where: Tc = time of concentration (min),

L = length of main channel (ft), and

h = height difference from the source to the exit along main channel (ft).

iii. Kerby-Hatheway Method

For small watersheds where overland flow is an important component, but the
assumptions inherent in the Morgali and Linsley approach are not appropriate, then
the Kerby (1959) method can be used. The Kerby-Hatheway equation is

Tc = (0.67NL)0.467
(√S) 0.467

Where: Tc = time of concentration (min),

N = Kerby roughness parameter (dimensionless),
S = overland flow slope (dimensionless).

Overland flow rarely occurs for distances exceeding 1200 feet. So, if the watershed
length exceeds 1200 feet, then a combination of Kerby’s equation and the Kirpich
equation may be appropriate. Certainly, the combination of overland flow and
channel tc is an appropriate concept. Values for Kerby’s roughness parameter, N,
are presented on table below.

Table 1: Kerby’s roughness parameter

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Description N

Pavement 0.02
Smooth, bare packed soil 0.10
Poor grass, cultivated row crops or moderately rough bare surfaces 0.20
Pasture, average grass 0.40
Deciduous forest 0.60
Dense grass, coniferous forest, or deciduous forest with deep litter 0.80

c) Runoff Coefficient

The runoff coefficient is the coefficient which is depend on the type of soil, topography
and vegetation characteristics of the catchment. The table below gives different values
of the coefficient depending on the catchment characteristics.

Table 2: Runoff coefficient

Description of area Runoff Coefficients (C)

Business:
Downtown 0.70- 0.95
0.50 - 0.70
Neighborhood area
Residential (Urban):
Single family area 0.30 - 0.50
Multi units detached 0.40 - 0.60
Multi units attached 0.60 - 0.75
Residential (suburb) 0.25 - 0.40
Apartment area 0.50 - 0.70
Industrial:
Light 0.50 - 0.80
Heavy 0.60 - 0.90
Parks, Cemeteries 0.10 - 0.25
Play grounds 0.20 - 0.35
Rail road yards 0.20 - 0.40
Unimproved area 0.10 - 0.30

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Source: Hydrology, Federal Highway Administration, HDS No. 2002, Second

edition.

Procedures of determining the design flood discharge

a) Determine time of concentration of your catchment

b) Determine the intensity of rainfall.
c) Determine the resultant runoff coefficient.
d) Determine the area of your catchment.
e) Select the design return period, T.
f) Finally, find the design flood discharge using the ration formula above.

The method was developed based on the following assumptions:

a) The rainfall intensity is the same over a duration of time equal or greater than the
concentration time
b) The soil properties are the same throughout the catchment area
c) The coefficient of runoff is independent of the intensity of rainfall
d) The drainage area is less than 1.2 km2.

Limitations of rational method

a) Estimation of tc especially critical on small watershed where tc is short and changes in

design intensities can occur quickly.
b) Reflects only the peak and gives no indication of the volume or the time distribution of
the runoff
c) Lumps many watershed variables into one runoff coefficient
d) Lends little insight into our understanding of runoff process, cases like watershed
conditions vary greatly across watershed.
e) The method is great oversimplification of a complied process
f) The application of ration method is normally limited to less than

2.4.1.2 Time-Area Method

The method was developed from modification of rational method. The method consists of
rainstorm profile combination with an incremental time-area diagram It consists of the

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combination of a rainstorm profile with an incremental time-area diagram (Stromwater Drainage

mannual, 2018). Given a rainstorm profile in which the average rainfall intensities within
successive time increments are i1, i2, i3, and the successive ordinates of the runoff hydrograph can
be written as.

Q1 = 0.278 C i1 A1
Q2 = 0.278 (C i1 A2 + C i2 A1)
Q3 = 0.278 (C i1 A3, + C i2 A2 + C i3 A1 …) etc.

Where: C = runoff coefficient

A1, A2, etc. = successive increments of the time-area.
The limitation and assumption of this method is the same as that of rational method.

2.4.1.3 Transport and Road Research Laboratory, TRRL

The budget in project construction of roads in East Africa a large proportion of the total cost is for
the construction of bridges and culverts to cross streams from small catchments. Whereas most of
the larger rivers in East Africa have flow measuring stations, very few smaller streams are so
equipped. Design methods must therefore be based on rainfall-runoff models This method was
developed for East African flood model on the basis of rainfall/runoff studies for the range of
selected catchments area of up to 200 km2. The procedures of using this model is fully described
in TRRL, Laboratory Report No. 706 and in subsequent publication. (Fiddes, 1976).

The following are procedures of using the TRRL method

1. Determine the catchment on large scale map and to measure catchment area, slope and
channel slope.
2. Inspection catchment type can be established in hence lag time, K

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Table 3: Catchment lag times

Catchment type Lag time (K) hrs.

Arid 0.10
Very steep small catchments (slopes> 20%) 0.10
Semi-arid scrub (large bare soil patches) 0.30
Poor pasture 0.50
Good pasture 1.50
Cultivated land (down to river bank) 3.00
Forest, overgrown valley bottom 8.00
Papyrus swamp in valley bottom 20.0
Source: TRRL Laboratory report 706

3. Investigation at the field the soil type can be described as in using Table 4: Standard
Contributing area coefficients with land slope of the catchment, the standard
contributing area coefficient (CS). Table 4: Standard Contributing area coefficients
4. By using Appendix 4 to fix antecedent rainfall zone and check in Table 3 to see if the
zone is wet, dry, or semi-arid.
5. To estimate catchment wetness factor (CW) from Table 5: Catchment wetness factor

Table 5: Catchment wetness factor

Catchment wetness factor

Rainfall Zone Perennial Streams Ephemeral Streams
Wet zones 1.00 1.0
Semi-arid zone 1.00 1.0
Dry zones (Except west Uganda) 0.75 0.5
West Uganda 0.60 0.3

6. From site inspection decide on type of vegetative cover, paying particular attention on
areas close to the stream. Using Table 6 estimate land use factor (CL)

Table 6: Land use factors

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Type of vegetation cover Land use factor, CL

Largely bare soil 1.50
Intense cultivation (particularly in valley) 1.50
Grass cover 1.00
Dense vegetation (particularly in valley) 0.50
Ephemeral stream, sand filled valley 0.50
Swamp filled valley 0.33
Forest 0.33

7. Determine contributing area coefficient (CA)

• CA = CS X CW X CL
8. Determination if initial retention, Y if antecedent rainfall zone in appendix 4 is semi-
arid or west Uganda, initial retention (Y) is 5mm. For all other zones, Y = 0.
9. Using appendix 4 estimate rainfall time TP and (n)

Table 7: Rainfall time for East African

Zone Index, n Rainfall Tp (hrs.)

Inland zone 0.96 0.75
Coastal zone 0.76 4.00
Kenya-Aberdar Uluguru Zone 0.85 2.00

10. To calculate base time (TB)

• TB = TP + 2.3K when TA = 0
11. Determine 2-year daily point rainfall (R2/24)
12. Determine 10 year: 2-year ration (Q) from of TRRL manual: For ten years flood.
13. Calculate 10-year daily point rainfall (R10/24)
• R10/24 = R2/24 (Q)
14. Calculate the storm rainfall during base time, RTB
• RTB = (TB/24) x 24.33/ (TB+0.33)) n x R10/24
15. Calculate area reduction factor, ARF
• ARF = 1-0.04 x TB-1/3 x A1/2

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16. Calculate average rainfall, P

• P = RTB x ARF
17. Calculate volume of runoff, RO
• RO = CA x P x A x 103
18. Calculate Average flow, QAV
19. Then recalculate base time, TB
• TB = TP + 2.3 x K + TA

Where TA = (0.028 x L)/QAV1/4 x S1/2

20. Repeat procedure number 14 up to 19 until when the QAV is within 5% of previous
estimate.
21. Then find the design flood, Q
• Q = F x QAV

Where: F is peak flood factor

F = 2.8 K < 0.5 hour
F = 2.3 K > 1 hour.

2.3.1.4 Unit Hydrograph

The concept of the unit hydrograph (UH) - developed in 1932 by Sherman (Camille Thomason,
2019); it is the representation of the direct runoff hydrograph (DRH) from the effective rainfall
hyetograph (ERH) at a specific location such that at the outlet of a watershed. Maximum watershed
size for the method (5000 km2).

According to (Raghunath, 2006) The Unit Hydrograph (UH) represents the DRH resulting from
one unit (1 in or 1 cm) of effective rainfall (ER) occurring uniformly over the watershed, at a
uniform rate during a specified duration of time.

Derivation of the unit hydrograph

a) Separate the base flow from the streamflow hydrograph.

b) Compute the Direct Runoff steam flow volume (area under Direct Runoff hydrograph) and
divide it by the catchment’s area to determine the effective rainfall depth

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c) Normalize the Direct Runoff hydrograph by dividing its ordinates by the effective rainfall
depth d. The result is a tr-Unit Hydrograph
d) Determine the effective duration of excess rainfall. To do this, obtain the
effective rainfall hyetograph and its associated duration. This duration is the duration
associated with the unit hydrograph.

The fundamental assumptions implicit in the use of unit hydrographs for modeling
hydrologic systems are:

a) Watersheds respond as linear systems. On the one hand, this implies that the
proportionality principle applies so that effective rainfall intensities (volumes) of different
magnitude produce watershed responses that are scaled accordingly. On the other hand, it
implies that the superposition principle applies so that responses of several different
storms can be superimposed to obtain the composite response of the catchment.
b) The effective rainfall intensity is uniformly distributed over the entire river basin.
c) The rainfall excess is of constant intensity throughout the rainfall duration.
d) The duration of the direct runoff hydrograph, its time base, is independent of the effective
rainfall intensity and depends only on the effective rainfall duration (Ramírez, 2010)

2.3.1.5 Empirical Methods

These are formula’s which are used to estimates the maximum flood discharge in river. The
followings are developed empirical formula’s which were developed based on different scenarios.
A is the area drainage basin in km2 and Q is the maximum flood discharge in cumec. (Raghunath,
2006)
a) Dicken formula’s
This type of empirical formula is used to find the discharge of moderate rivers (basins).
The formula is given as

Q = CDA3/4

Where CD is the coefficient depend on average annual rainfall (aar).

For actual use the local experience will be of the aid in the proper selection of Cd Dicken
formula is used in the central and Northern part of India

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 Final year Project I

b) Myles formula
The formula of finding the maximum discharge is given as Q = √175A

c) Fuller’s formula (1914)

This formula was developed from USA basins, which requires 10 years data for the
sufficient reliability. The formula is given as

Q = CA0.8(1+0.8logTT) (1+2.67A-0.5).

The coefficient, C varies from 0.026 up to 2.77. T is the recurrence interval in years.

d) Creager’s formula

The formula is used in USA and is given as

Where: C is the coefficient which is equal to 130 or 150.5 for areas most favourable
to large floods.

2.4 Method of sizing cross drainage structures

Sizing of culvert involves three different methods. The selection of the method depends on the
data available and the nature of the project.

2.4.1 Manning’s equation

The method was found in 1970 which was developed from Chezy equation. The Manning
formula is used in sizing the different drainage structure. The formula is given by:

2 1
A.R ⁄3 .S ⁄2
Q=
n

Where: Q = discharge capacity,

A = Cross sectional area of the structure of the structure,
R =Hydraulic radius given by cross-section area divided by wetted perimeter,
n = Manning’s roughness coefficient,

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 Final year Project I

S = Slope of the drainage structure (bed slope).

The manning’s roughness coefficient depends on different type of material in construction the type
of drainage structure. Coefficient can be obtained as shown in a Table 8.

Table 8: Manning's coefficients

Surface material Manning’s coefficient, n

Asbestos cement 0.011
Asphalt 0.016
Brick 0.015
Concrete (cement finished) 0.012
Clay tile 0.014

The slope of drainage structure is calculated by the ration of heights to the distance at the inlet to
outlet. Slope is a bed slope of the drainage structure.

2.4.2 Nomograph

The was developed by Federal Highway Administration (FHWA) estimation of capacity of culvert.
This method used to determine the culvert diameter based on calculating the design discharge and
the headwater depth such that ration between headwall to diameter ratio.

The following are procedure of determine the size of opening that required to pass the design
discharge.

i) Determine the design discharge that passes through the outlet at the crossing.
ii) Determine the culvert entrance type from the three types of entrance as described in figure
4. The choice of the culvert entrance depends on the uses of the culvert, location and also
material availability.
iii) Determine the headwater depth ratio for the proposed stream that crossing. The headwater
depth ratio is the ratio Hw/D where the Hw is the headwall depth from the height of the fill
where water begins to spill out of the crossing to the bottom of culvert invert. D is the
diameter or rising of culvert inlet.

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 Final year Project I

iv) To size a projecting inlet culvert, place a straight edge connecting the “Headwater Depth
ratio of 1 on the projecting inlet scale at through the design discharge of calculated for the
proposed stream.
v) Read off the need culvert diameter on the left scale of the nomograph.

Consider the nomograph chart a figure below which is show sizing of culvert using headwall as
the type of entrance. As described in the procedure above the headwater depth to diameter ratio
was ration was chosen to be less than one and the design discharge of 200 cfs. The result of size is
and the 76 inches.

Figure 4: Nomograph
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 Final year Project I

2.5 Performance analysis of drainage structure

2.5.1 Hydraulic Performance of Culvert

According to (Works, Introduction, and Hydraulics 2000) Culvert is a drainage structure which
is constructed under roadways to provide cross drainage when a stream or a river cross the
alignment of road. Culverts and bridges perform similar tasks but their difference lies mainly in
the size, but the bridges usually used to accommodate longer spans.

After performing hydrological analysis to determining the quantity of water which will pass
through the outlet point of at a particular area, the next step is to propose the sufficient capacity of
cross drainage to accommodate the design discharge. Drainage structure positioning generally
increases the velocity of flow above that in the natural channel (Nwaongazie & Agiho, 2019). High
velocity is critical immediately downstream of the culvert outlet and the scour potential from the
resulting energy is the factor to be considered in culvert design. When the waterway area of culvert
is less than the cross-section area of upstream channel, the water will submerge the inlet and might
reach levels higher than the road as the resulting in an overtopping of the structure. The culvert
should be designed to carry the design discharge with a headwater depth.

The water velocity in a culvert basically depends on the flow velocity of upstream (inlet),
geometric design of upstream and downstream, the gradient of the culvert, size and shape of the
culvert cross section area, roughness of the pipe material surface, headwater to culvert depth ratio,
and the flow velocity at the downstream. Scour velocity is defined as the critical speed of flow at
which the erosion of the earth surface occurs.

2.5.2 Location of Culverts

Culvert location deal with both vertical and horizontal alignment of the culvert with respect to road
and stream. The location of the culvert is important for hydraulic performance, stream stability,
construction and maintenance costs and prevention of damage by erosion (FHWA, Hyraulic
Design of Highway culverts, 2012). The culvert location should follow the existing alignment of
the stream unless the improvement of the alignment is done. The gradient of the culvert is one of
the most important tools during the position of the culvert, the culvert should follow the gradient

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 Final year Project I

of the stream in order to avoid the encouragement of erosion of the stream bed and the outlet. If
the gradient is very small sedimentation may occur(Works, Introduction, and Hydraulics 2000).

The location of the culvert invert must be set at the same level as the that of stream bed. When a
stream and road interact sometimes it is important to stabilize a shifting channel or to improve the
geometry of the channel. This will avoid bend at start and end of the culvert because the abrupt
change in direction of the stream will cause the flow to be turbulence and hence increasing scouring
and sedimentation in some parts of the stream.

2.5.3 Deposition in the culvert

Occurs because the capacity of the flow within the culvert to transport the sediment is less than
that of the stream (Camille Thomason, 2019). Deposition in the culvert can be caused when the
culvert cross section is greater than that of the stream, abrupt change in flow direction, also the
gradient of culvert, the location of the culvert. The culvert must be able to self-cleansing in order
to archive this the velocity of water within the culvert should be designed.

Types of Culverts

The selection of culvert in of a location is dependent upon the hydraulic requirement as well as the
strength required to sustain the weight of fill and traffic load. There are several types of culverts
which is used in road construction:

a) Pipe culvert
b) Box culvert

c) Arch culvert
d) Bridge culvert

2.5.4 Inlet and outlet controls

The analysis of flow characteristics in a culvert is based on a computation of energy potentials at

various points along the watercourse. The analysis use energy line diagrams to show the results.
Consider the figure below which show the assessment of energy required to pass a given quantity
of water through a culvert.

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 Final year Project I

2.5.5 Energy Dissipation

It is very important to control the flow velocity at the outlet point. High flowing velocity means
that the energy of flowing is high. The energy of the discharge must be dissipated or broken. It is
very important to determine the distance in which is sufficient to dissipate the energy. There are
various technique employed to dissipate the energy. Technique used are Rip-rap, stone lining and
casted energy dissipated(Works, Introduction, and Hydraulics 2000).

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 Final year Project I

CHAPTER 3: DATA AND METHODOLOGY

3.1 Description of Project Area

3.1.1 Location

The location of the proposed project is Mabatini ward which is in the Mwanza city. The map in
Figure 5 shows the location of a project where the existing drainage structure located with local
coordinate system.

Figure 5: Map of a project area

Mwanza City is located on the southern shores of Lake Victoria in Northwest Tanzania. It
covers an area of 256.45 Kilometer square of which 184.90 (72 percentages) is dry land and
71.55 Kilometer (28 percentages) is covered by water. Of the 184.90-kilometer dry land area,
approximately 173 kilometer is urbanized while the remaining areas consist of forested land,

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 Final year Project I

valleys, cultivated plains, grassy and undulating rocky hill area (Mwanza Region Socio-
Economic Profile, 2017)

3.1.2 Topography

The topography of the study area is characterized by gently undulating granites and granodiorite
physiography with isolated hill masses and rock inselbergs.it is also characterized by well
drained sand loamy soil generated from coarse grained cretaceous. The streams flow into Lake
Victoria. The vegetation cover is typical savannah with scattered tall trees and grass (Mwanza
Region Socio-Economic Profile, 2017).

3.1.3 Demographic Characteristics in Mwanza

According to the 2002 and 2012 Population Censuses reports, the population of Mwanza City
increased from 241,923 (119,617 male and122,305 female) in 2002 and reached 363,452
(177,812male and 185,578female) in 2012 with the annual natural growth rate of 3.0
percent (MWAUWASA, 2013).

3.1.4 Climate

Mwanza City lies at an altitude of 1,140 meters above the sea level with mean temperature
ranges between 25.7OC and 30.2OC in hot season and 15.40C and 18.6OC in the cooler
months. The City also experiences the average annual rainfalls between 700 and 1000 mm
falling in two fairly distinct seasons, short and long rainfalls. The short rain season occurs
between the months of October and December and long rain season last between February
and May (Mwanza Region Socio-Economic Profile, 2017).

3.2 Desk study

This will involve the revision of well-established scholarly articles, books and other sources which
are relevant to a particular issue, area of research, or theory, providing a description, summary,
and critical evaluation of each objective. The purpose is to offer an overview of significant
literature published on a topic. The aim of literature review is to explore the background of the
problem and the extent of existence.

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 Final year Project I

3.3 Field investigation

Field investigation is will involve the study of existing drainage structure condition which is used
to determine the overall condition of the drainage structure. the objective of this is to determine
the overall condition of the existing culvert which will be rate the assessment mode will involve
the use the Federal Highway Administration manual for culvert. Also, through field investigation
type and dimension of existing drainage will be determined.

3.3.1 Field investigation data

The data will be corrected through site inspection and measurement. The objective is to determine
if the culvert needs repair, rehabilitation, and alignment modification depending on the condition.
The data which will be collected on the site for assessing the general condition of culvert will be
as follow:

3.3.1.1 Data required and collection

a) Dimension of existing cross drainage structure

The dimension of existing cross drainage structure will be collected by measuring the
physical dimension of the structure. The mode of collecting data will be collected by
measuring the dimensions of cross section of a structure. the data which will be corrected
is length, width and height of the existing cross drainage structure.
b) Condition assessment
The data required for assessment will be obtained by inspection of the existing cross
drainage structure
• Observation of overall condition
• Culvert barrel
• Headwalls and wing walls
• Water way adequacy
• Approach road and embankment

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 Final year Project I

3.3.1.2 Data analysis

a) Dimension of existing structure

This data will be used to determine the cross-sectional area of the existing cross drainage
structure. the objective of determine the area is to check if the existing cross drainage
structure is adequate to pass the design discharge or not.
b) Condition assessment
Rating system of ten-point scale form Federal Highway Manual for culvert (FHWA, 1986)
will be used to determine the condition of the existing structure. The forms of assessment
are attached in appendix 2 and 5.

3.4. Estimation of design discharge at the location of assessment.

The design discharge will be determined by using Transport and Road Research Laboratory
method (TRRL). The determination of discharge will follow of TRRL procedure as describe as in
this report but the rainfall data will be collected from the weather station near the project area.

3.4.1 Data Required and Collection

Catchment Data.
Catchment data which are required in determination of design discharge at the location assessed
using the TRRL method are classified explained as follow.
a) Area of a catchment
The catchment area will be demarcated using GIS. Source of data is DEM which will be
corrected from free available SRTM with resolution of 90km. The area will be measured
in square kilometers (km2). Measurement of catchment area will be carried out in GIS
software.
b) Channel slope
The slope of a channel will be collected from channel generated on GIS map of the
catchment area. The slope is obtained as the ration between the difference of points of
outlet and the starting points of the channel.

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 Final year Project I

c) Channel length.
The length of a channel will be measure from outlet point of the catchment to the starting
point of the channel of most remoting position of the catchment. This data is collected from
GIS map of the catchment area. This involve measuring the length of a channel.
d) Land slope.
The land slope will be taken as the channel slope such that the slope is obtained as the
ration between the difference of points of outlet and the starting points of the channel of
most remoting position of the catchment.

Soil Type
Catchment Type Well Drained Slightly impeded Impeded
drainage drainage
Very Flat < 1.0% 0.15 0.30
Moderate 1-4% 0.09 0.38 0.40
Rolling 4-10% 0.10 0.45 0.50
Hilly 10-20% 0.11 0.50
Mountainous > 20% 0.12
e) Soil type
The type of soil will be determined from site investigation. The soil type will be classified
according to guideline of TRRL manual as described in appendix 3 of this report.
f) Catchment type,
The catchment type is determined from the manual of TRRL as described in Table 3. The
site inspection is first conducted then classification of the type follow.
g) Rainfall zone
The rainfall zone is determined from the manual of TRRL as described in appendix 4 of
this report.
h) Rainfall time
The rainfall time is determined from the manual of TRRL.
i) Land use
The land use of catchment will be obtained from the map on TRRL manual which is in
Table 6 of this report.

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 Final year Project I

Type of vegetation cover Land use factor, CL

Largely bare soil 1.50
Intense cultivation (particularly in valley) 1.50
Grass cover 1.00
Dense vegetation (particularly in valley) 0.50
Ephemeral stream, sand filled valley 0.50
Swamp filled valley 0.33
Forest 0.33

j) lag time, K
The lag time can be determined as described in

Catchment type Lag time (K) hrs.

Arid 0.10
Very steep small catchments (slopes> 20%) 0.10
Semi-arid scrub (large bare soil patches) 0.30
Poor pasture 0.50
Good pasture 1.50
Cultivated land (down to river bank) 3.00
Forest, overgrown valley bottom 8.00
Papyrus swamp in valley bottom 20.0
Table 3.

k) Rainfall data.
The rainfall data that required in the analysis will be collected from nearby station which
is located near the project area. The source of data that will be used in analysis is from
Tanzania Metrological Authority.

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 Final year Project I

3.4.2Data analysis

3.4.2.1 Contribution of area coefficient

The catchment data will be used to determine the contribution of area coefficient to the discharge,
rainfall base time and rainfall zone. Each catchment data has function in the determination of
discharge. The contribution of area coefficient, CA is given as
• CA = CS X CW X CL

Where: CS = Standard contributing area coefficient obtained from catchment slope

CW = Catchment wetness factor obtained from rainfall zone and type of stream
CL = Land use factor obtained from land use information

3.4.2.2 Rainfall data

The analysis of rainfall data at the return period of 2,10, 25 ,50 and 100 year will be analyzed using
extreme value of Type I known as Gumbel distribution. The process of determine the rainfall storm
using the extreme value type I. after determination of design storm for different design period then
the calculation for average rainfall storm will be calculated according to TRRL manual. The
procedures area as follow:
The prediction equation of design rainfall storm at a certain return period is given as:

PT = u + .yT
Where PT = rainfall storm magnitude of a certain return period.
yT = Frequency factor.

The estimation of parameter from method of moment gives

−
Mean: 𝑥 = 𝑢 + 0.5772𝛼
standard deviation: 𝑠 = 1.28𝛼
Mean is obtained from the take average rainfall of the sample and s is the standard deviation of
the sample.
Determination of Calculate the storm rainfall during base time, RTB

• RTB = (TB/24) x 24.33/ (TB+0.33)) n x PT

Determination of area reduction factor, ARF

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 Final year Project I

• ARF = 1-0.04 x TB-1/3 x A1/2

Calculate average rainfall, P

• P = RTB x ARF

3.4.2.3 Design discharge, Q.

The volume of runoff, RO is given by:

• RO = CA x P x A x 103

Where: P is average Rainfall

A area of catchment
CA is coefficient of area contribution
The calculation of average flow, QAV is given by:
• QAV = (0.93/3600) x (RO/TB)

Recalculate the base time TB which is given as:

• TB = TP + 2.3 x K + TA

Where: TA is TA = (0.028 x L)/QAV1/4 x S1/2

The design discharge Q is given as the design flood, Q

• Q = F x QAV

Where: F is peak flood factor

F = 2.8 K < 0.5 hour
F = 2.3 K > 1 hour (Fiddes, 1976)

3.5 Propose of appropriate size of cross drainage structure.

The Manning formula will be used in sizing the t drainage structure. The formula is given by:

2 1
A.R ⁄3 .S ⁄2
Q=
n

Where: Q = design discharge.

A = Cross sectional area of the structure of the structure,
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 Final year Project I

R =Hydraulic radius given by cross-section area divided by wetted perimeter,

n = Manning’s roughness coefficient,
S = Slope of the drainage structure (bed slope).

3.5.1 Data required and collection

The manning’s roughness coefficient depends on different type of material in construction the type
of drainage structure. Coefficient can be obtained as shown in a Table 8.

Table 9: Manning's coefficients

Surface material Manning’s coefficient, n

Asbestos cement 0.011
Asphalt 0.016
Brick 0.015
Concrete (cement finished) 0.012
Clay tile 0.014

The slope of drainage structure is calculated by the ration of heights to the distance at the inlet to
outlet. Slope is a bed slope of the drainage structure. Slope, S is longitudinal slope will be taken
as the same as that of the channel.

3.5.2. Data Collection:

Collection of data will be carried at field and then analysis will be carried out.

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 Final year Project I

REFERENCES
1. Camille Thomason, P. (2019). Hydraulic Design Manual. Texas: Texas Department of
Transportation.
2. Chow, V. T. (1988). Applied Hydrology. (B. J. Morriss, Ed.) Singapole: McGraw-Hill
Publishing Company Limited.
3. FHWA. (1986). Culvert Inspection Manual . Virginia : Federal Highway Administaration
.
4. FHWA. (2012). Hyraulic Design of Highway culverts (Third edition ed.). Virginia :
Federay Highway Administration .
5. Fiddes, D. (1976). Transport and Road Research Laboratory. Berkshire: Crownthorne
Publishers.
6. Garg, S. K. (1976). Irrigation Engineering and Hydraulic Structures . Delhi: KHANNA
Publisher .
7. Kwast, D. H. (n.d.). QGIS and Open data for Hydrological Applications.
8. (2017). Mwanza Region Socio-Economic Profile. Mwanza .
9. MWAUWASA. (2013). Environmental Impact asssessment for construction of sewage
water system for Mabatini and Igogo areas in Mwanza city. Mwanza: Mwanza Urban
Water and Sewerage Authority.
10. Nwaongazie, I. L., & Agiho, G. C. (2019). Perfomance analysis of Box and circular
culvert Using HY 8 software . Nsukka: Nigerian Journal Technology .
11. Raghunath, H. K. (2006). Hydrology 2nd edition . New age international (T) ltd .
12. Stormwater Drainage Manual (Fifth Edition ed.). (2018). Hong Kong: Goverment of the
Hong Kong .
13. Subramanya, K. (2008). Engineering Hydrology. the Tata McGraw-Hill Publishing
Company Limited.

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Appendex 1: Map of Cathcment Area

Area = 20.23 km2

Length of a channel = 6.54km

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 Final year Project I

Appendex 2: Form of Assessing Condition of Culvert

Source: (FHWA Culvert Inspection Manual (1986))

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 Final year Project I

APPENDEX 3: Soil Zone

Source: (TRANSPORT and ROAD Department of the Environment TRRL LABORATORY REPORT 706 THE
TRRL
EAST

AFRICAN FLOOD MODEL by D Fiddes , Berkshire ISSN 0305-1293 CONTENTS 1976)

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 Final year Project I

APPENDIX 4: Rainfall Zone

(TRANSPORT and ROAD Department of the Environment TRRL LABORATORY REPORT 706 THE
TRRL EAST AFRICAN FLOOD MODEL by D Fiddes , Berkshire ISSN 0305-1293 CONTENTS 1976)

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 Final year Project I

APPENDIX 5: Rating System

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 Final year Project I

Working Plan and Budget

39